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https://github.com/nocotan/geodesical_skew_divergence
PyTorch implementation of α-geodesical skew divergence
https://github.com/nocotan/geodesical_skew_divergence
divergence information-geometry js-divergence kl-divergence machine-learning statistics
Last synced: 3 months ago
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PyTorch implementation of α-geodesical skew divergence
- Host: GitHub
- URL: https://github.com/nocotan/geodesical_skew_divergence
- Owner: nocotan
- License: mit
- Created: 2021-03-29T08:45:17.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2021-07-05T23:36:07.000Z (over 3 years ago)
- Last Synced: 2024-07-05T06:02:22.725Z (4 months ago)
- Topics: divergence, information-geometry, js-divergence, kl-divergence, machine-learning, statistics
- Language: Python
- Homepage:
- Size: 1.85 MB
- Stars: 10
- Watchers: 2
- Forks: 1
- Open Issues: 6
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-information-geometry - geodesical_skew_divergence
README
# α-Geodesical Skew Divergence
[](https://github.com/nocotan/geodesical_skew_divergence/blob/main/LICENSE)
[](https://pypi.org/project/gs-divergence/)
[](https://arxiv.org/abs/2103.17060)
[](https://pepy.tech/project/gs-divergence)
Official PyTorch Implementation of "[α-Geodesical Skew Divergence](https://www.mdpi.com/1099-4300/23/5/528)".
- [[Entropy](https://www.mdpi.com/1099-4300/23/5/528)]
- [[arXiv](https://arxiv.org/abs/2103.17060)]
> The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.
## Installation
### From PyPI
Install gs_divergence from PyPI via
```bash
$ pip install gs_divergence
```
### From GitHub
Alternatively, you can install the latest version directly from the GitHub repository with the following command.
```bash
$ git clone https://github.com/nocotan/geodesical_skew_divergence
$ python setup.py install
```
## Usage
### Compute divergence from two Tensors
```python
import torch
from gs_divergence import gs_div
a = torch.Tensor([0.1, 0.2, 0.3, 0.4])
b = torch.Tensor([0.2, 0.2, 0.4, 0.2])
div = gs_div(a, b, alpha=-1, lmd=0.5)
```
### Compute gradients
```python
import torch
from gs_divergence import gs_div
a = torch.tensor([0.1, 0.2, 0.3, 0.4], requires_grad=True)
b = torch.tensor([0.2, 0.2, 0.4, 0.2])
div = gs_div(a, b, alpha=-1, lmd=0.5)
dif.backward()
```
| parameter | description |
|-----------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| input | Tensor of arbitrary shape |
| target | Tensor of the same shape as input |
| alpha | Specifies the coordinate systems which equiped the geodesical skew divergence (default=``-1``) |
| lmd | Specifies the position on the geodesic (default=``0.5``) |
| reduction | Specifies the reduction to apply to the output: ``'none'`` \| ``'batchmean'`` \| ``'sum'`` \| ``'mean'``. ``'none'``: no reduction will be applied ``'batchmean``': the sum of the output will be divided by the batchsize ``'sum'``: the output will be summed ``'mean'``: the output will be divided by the number of elements in the output default=``'sum'`` |
## Definition of α-Geodesical Skew Divergence
## Visualizations of the α-Geodesical Skew Divergence
### Monotonicity of the α-geodesical skew divergence with respect to α
### Continuity of the α-geodesical skew divergence with respect to α and λ.
## Citation
```bibtex
@Article{e23050528,
AUTHOR = {Kimura, Masanari and Hino, Hideitsu},
TITLE = {alpha-Geodesical Skew Divergence},
JOURNAL = {Entropy},
VOLUME = {23},
YEAR = {2021},
NUMBER = {5},
ARTICLE-NUMBER = {528},
URL = {https://www.mdpi.com/1099-4300/23/5/528},
ISSN = {1099-4300},
ABSTRACT = {The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.},
DOI = {10.3390/e23050528}
}
```